Molecular speeds: The root-mean-square speed (thermal speed) of the molecules of a gas is 200 m/s at 23.0°C. At 227°C the root-mean-square speed (thermal speed) of the molecules will be closest to
A) 160 m/s
B) 330 m/s
C) 260 m/s
D) 630 m/s
E) 2000 m/s

Question

Quizplus · Accepted Answer

The root-mean-square speed of gas molecules is proportional to the square root of the absolute temperature (Kelvin). Converting temperatures to Kelvin: 23°C = 296 K and 227°C = 500 K. The ratio of speeds is √(500/296), which gives approximately 1.3. Multiplying 200 m/s by 1.3 gives approximately 260 m/s.

Molecular Speeds: the Root-Mean-Square Speed (Thermal Speed) of the Molecules